Positive Solutions of Annular Elastic Membrane Problems with Finite Rotations
Hans Grabmüller, Robert Pirner · Studies in Applied Mathematics · 1987
Following the study of axisymmetric deformations of annular membranes under a normal surface load on the basis of the Föppl‐Hencky small‐finite‐deflection theory, which has been completed in recent works, the corresponding methods are here generalized as to apply to finite‐deformation problems of the Simmonds‐Libai simplified Reissner equations of finite rotations. The question of uniqueness of positive regular solutions is solved in general, and an integrale‐quation technique is developed which yields existence and nonexistence results for an extensive range of the boundary data where previous investigations failed. In contrast to the Föppl theory, some of the boundary conditions are nonlinear, and hence an extension to the finite‐rotation case is not straightforward. Moreover there are significant differences between the small‐ and the finite‐rotation theory.